Question

Train A leaves Ludhiana for Delhi at 11 am running at a speed of $60\text{ km/hr}$. Train B leaves Ludhiana for Delhi by the same route at 2 pm on the same day, running at a speed of $72\text{ km/hr}$. At what time will the two trains meet each other?
A. 5am on the next day
B. 2am on the next day
C. 5pm on the next day
D. 2pm on the next day

Answer 1

The concept of relative speed is used when two or more bodies moving with some speeds are considered. To make things simpler, one body can be made stationary (i.e., speed is zero) and take the speed of the other body with respect to the stationary body, which is the sum of the speeds if the bodies are moving in the opposite direction and the difference if they are moving in the same direction. This speed of the moving body with respect to the stationary body is called the relative Speed.

Complete answer:
Observing the given question, let us assume the given data:
Speed of train A, ${{v}_{1}}=60\text{ km/hr}$,
Speed of train B, ${{v}_{2}}=72\text{ km/hr}$.
It is also given in the question that both train A and train B leave to Delhi following the same route that implies their direction of path is the same.
Train A leaves Ludhiana at 11am and Train B leaves at 2pm the same day.
Train A leaves before Train B, which implies train A leaves 3 hours before train B leaves.
We know that, $\text{Speed = }\dfrac{\text{Distance}}{\text{Text}}\Rightarrow \text{Distance = Speed }\times \text{ Time}$. So, the distance travelled by train A before Train B departs will be,
$\begin{aligned} & \Rightarrow \text{ Distance = speed of A }\times \text{time taken} \\\ & \Rightarrow \text{ Distance = }60\times 3=180\text{ km} \\\ \end{aligned}$
Suppose two bodies are moving at a different speed in the same direction.
Let the speed of the 1st body be $x\text{ km/hr}$ and the speed of the 2nd body be $y\text{ km/hr}$.
So, their relative speed is equal to $\left( x\text{ }\text{ }y \right)\text{ km/hr}$ if $x>y$.
Using the above formula for train A and train B, their relative speed will be equal to $\left( 72\text{ }\text{ }60 \right)\text{ km/hr }=\text{ }12\text{ km/hr}$.
The time after which both the bodies meet is equal to $\text{ t=}\dfrac{\text{distance travelled}}{\text{relative speed}}\text{ }$. Then, we get.
$\Rightarrow t=\dfrac{180}{12}=15hrs$
Here, the total time taken will be $2\text{ pm }+\text{ }15\text{ hrs}$. That is,
$\Rightarrow 2\text{ pm }+\text{ }15\text{ hrs }=\text{ }5\text{ am}$on the next day.
$\therefore$ The two trains will meet each other at 5am the next day.
Hence, option A is correct.

Note:
Students wouldn’t get the idea of relative speed in the first attempt, problems of this kind should be practiced so that the concept would be graspable. For, counting the number of total hours it would be useful to properly know the clock timings, or drawing a small clock would also be helpful for better calculations.